What is the line integral of vector field F = (x – y)i + (x+ y)j along the path shown below. (1,1) -y = x?
Q: Two protons (mass m = 1.7 x 10-27 kg, electric charge q 1.6 x 10-19 C) live in the xy plane. Proton…
A: Given: Charge, q = 1.6×10-19 Cmass, m =1.7×10-27 kgdistance, r1 =1×10-6, 0, 0 r2 =0,…
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Q: ne flux of the vector field F = 2x²y i +3³z2 j + 2z k through the circle of radius o the plane z = 2…
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Q: Find the k-component of (curl F) for the following vector field on the plane. F = (xe)i + (8y ex)j…
A: The vector field on the plane is given as F=xeyi^+8yexj^
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Q: Because the formulas for Coulomb's law and Newton's law of gravity have the same inverse-square law…
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Q: Problem 1.2.3. Three particles with equal positive charge q are at the corners of a square of side…
A: Three particles with equal positive charge q are at corners of square of side 'd'.(a). The fourth…
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Q: Evaluate both sides of the Divergence Theorem of the given vector field D = ye* ax + z(xy)? ay + (x…
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Q: Suppose the vector field F takes the values shown in the table below. Sketch this vector field on a…
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Q: Calculate the gradient V(x,y,z) for the scalar field (x,y,z) defined as (x, y, z) = 32xz + 18yz3 +…
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Q: 2. Show that F is a F(x, y, z) = (e)i + (xey + ez)j + (yez)k and C is the line segment from (0, 2,…
A: If a force is , F→=Mi⏜+Nj⏜+Pk⏜it will be a conservative field only and only if∂M∂y=∂N∂x , ∂N∂z=∂P∂y…
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Q: Consider the scenario shown below. Let a = 1.60 m, and i = 1.40 A. Determine the magnitude of the…
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Q: Compute the flux of the vector field F = 2zk through S, the upper hemisphere of radius 6 centered at…
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Q: Four stationary electric charges produce an electric field in space. The electric field depends on…
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- Consider the vector field ʊ(r) = (x² + y²)êx + (x² + y²)êy + z²êz. Decompose the vector field (r) into the sum of two other vector fields, a (r) and 5(r), such that a(r) has no divergence (it is solenoidal) and 5 (r) has no curl (it is irrotational). The answer is not unique. This is the Helmholtz decomposition.We have calculated the electric field due to a uniformly charged disk of radius R, along its axis. Note that the final result does not contain the integration variable r: R. Q/A 2€0 Edisk (x² +R*)* Edisk perpendicular to the center of the disk Uniform Q over area A (A=RR²) Show that at a perpendicular distance R from the center of a uniformly negatively charged disk of CA and is directed toward the disk: Q/A radius R, the electric field is 0.3- 2€0 4.4.1bConsider the following situation. A positive charge q is located a distance R from a charged wire bent into a circular arc as drawn. The arc has radius R, a net positive charge Q, and an angular extent of 30° (T/6 radians) centered on the same axis as q. 15° a. Calculate the electric field (vector) the arc of wire produces at q's location. Give the vector in component form. The vector only has one component. You should write down in words an argument using the problem's symmetry for this. b. Find the net force (vector) on q by the arc of wire. Give the vector in component form. c. Compare this force to the force produced by a positive point charge Q located a distance R away from q. Which force is greater, (b) or (c), and by what fraction? Show this algebraically.
- Solve 4,5Calculate the flux of the vector field F(x, y, z) = 5i + 5j + zk through the closed circular cylinder of radius 4 centered about the z-axis for -6 ≤ z < 6, oriented away from the z-axis. Note: a closed cylinder has a top and a bottom. Flux = SS F.dĀ=Evaluate the surface integral F⚫ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = −xi - yj + z³k, S is the part of the cone z = √x² + y² between the planes z = 1 and z = 4 with downward orientation ZA z = √√x² + y² xx 0 z=4